Algebra-2

Let's analyze the function and evaluate each of the statements:

Does it pass through (0, 0)?

The function is only defined for because logarithms are undefined for non-positive values of .

Specifically, is undefined at , so the graph does not pass through (0, 0).

Does it have a horizontal asymptote at ?

A logarithmic function like does not have a horizontal asymptote. As , , and multiplying by 3 causes the function to increase without bound. Therefore, it does not approach any finite value, and the horizontal asymptote is not at .

Is it always decreasing?

The function